Hypothesis testing analysis and unknown parameter estimation of GPS signal detection

Hypothesis testing analysis and unknown parameter estimation of both the intermediate frequency (IF) and baseband GPS signal detection are given by using the generalized likelihood ratio test (GLRT) approach, applying the model of GPS signal in white Gaussian noise. It is proved that the test statistic follows central or noncentral F distribution. It is also pointed out that the test statistic is nearly identical to central or noncentral chi-squared distribution because the processing samples are large enough to be considered as infinite in GPS acquisition problem. It is also proved that the probability of false alarm, the probability of detection and the threshold are affected largely when the hypothesis testing refers to the full pseudorandom noise (PRN) code phase and Doppler frequency search space cells instead of each individual cell. The performance of the test statistic is also given with combining the noncoherent integration.